A size-structured model for membrane filtration

In this talk, we present a novel size-structured framework to describe the operation of a filter in which we treat the pore size and particle size as independent variables. The resulting model is a differential-algebraic-integro system of equations, which incorporates particle capture by blocking (where particles become trapped when they encounter holes that are too small to pass through) and deposition (where particles stick to the porous structure). We illustrate the power of the model in several simple configurations, and use this to draw conclusions about filter behaviour and advantageous operating strategies.